ARTS & IDEAS/CULTURAL DESK

CONNECTIONS; Together, the Rational and the Spontaneous Can Make Sweet Illogic

By Edward Rothstein (NYT) 1072 words

This is the type of triangle that lies under David Auburn's acclaimed play about a mathematician's daughter, ''Proof,'' that opened this fall on Broadway. It is also found in Rebecca Goldstein's lyrical, affecting novel about a trio of physicists in ''Properties of Light.''

Such a conjunction of patterns might seem to be mere chance, perhaps, the way distant cloud chambers might display seemingly identical trails of particles. After all, the subterranean psychology at work in these triangles is no mystery. Since Plato, too, teaching has been thought to have an erotic character; so why shouldn't parental teaching be tangled up in dependence and discipleship?

Some of the coincidence is also due to contemporary preoccupations with gender. Where have women been found in the history of science? As muses to men? As uncredited providers of men's ideas? As autonomous creators denied their opportunities? Recent study of Einstein's relationships, for example, have ranged from speculation that his first wife was a co-creator of the theory of relativity, to, more soberly, ''Einstein in Love'' by Dennis Overbye (deputy science editor of The New York Times), in which Einstein's erotic life is knit into a biography.

But these lovers' triangles also overlap in a much more important way. For a long time, science and love were unrelated at best, conflicting at worst. In the 1938 comic film, ''Bringing Up Baby,'' for example, Cary Grant's respectable, reasonable paleontologist could unite with Katharine Hepburn's impulsive and passionate character only by turning his back on desiccated dinosaur bones. By the movie's end, an entire skeleton collapses under the weight of their embrace. Science's hard, cruel rationalism and love's impulsive freedom may be beyond reconciliation.

Now, the union is taking place, but under different conditions. Science and love, it seems, are haunted by similar questions. In both the very notion of truth is up for grabs.

And reason doesn't provide much reassurance. In ''Proof,'' the daughter worries that she, like her father, is on the verge of insanity; the issue comes up for the young physicist in ''Properties of Light'' as well. Interestingly enough, both figures, doubting their own sanity, consider the same sophistical proof that they are indeed sane: if they weren't they wouldn't be asking the question.

That is far from a convincing conclusion, because there is so little certainty to be had elsewhere. The creaky plot of ''Proof'' hangs on whether a particularly brilliant proof was the work of the prodigious daughter or her father. Once the father is dead, is there a convincing proof of authorship? Will handwriting analysis give an answer? Or styles of argument? Or the loyalty or disloyalty of the disciple-lover? The proof of the proof's identity is finally, as the mathematicians say, fairly trivial. It used some newer techniques the senior mathematician probably couldn't have learned -- a resolution too flimsy for the issues posed.

In ''Properties of Light,'' though, Ms. Goldstein strikes both deep and hard at the question by carefully circumscribing the lover's triangle within a crisply drawn scientific circle. A primary question facing contemporary physics is how to reconcile the two great theories of the last century: quantum mechanics and relativity. Each of the three main characters is trying to prove that despite influential interpretations of quantum theory, there are indeed objective truths to be found, that matter is something more than a probabilistic cloud, and that the observer is not the crucial figure in the workings of the universe.

In nonscientific communities, the young physicist points out, the ''difference between those who are committed to an independently existing reality and those who are not is roughly correlated with the distinction between the sane and the psychotic.'' In scientific communities, the situation is roughly reversed. In this lovers' triangle, the joint ambition is to make the universe seem less loony and ''put the psychosis back in the psyche, where it belonged.''

But the book itself becomes a demonstration of just how difficult the task is. ''I trust almost nobody,'' says the troubled daughter. ''I don't even trust the universe.'' The almost gothic plot strips away the powers of reason. Argument turns to whine and becomes futile in the face of madness. The ambiguities inherent in subatomic particles' location and movement are reflected in the ambiguous location and movement of the characters. And while Madame Blavatsky-style mysticism is ridiculed, even the devotees of ''independently existing reality'' may eventually give it credence.

What drives each of the characters in their stunted, pained existence is desire. It is partly the erotic desire the senior physicist believes spurs creation, but it is also the almost unrelenting desire to know, to be able to state with some clarity that this is how the world is, that it is possible, given the time and the vision, to make sense of things. This is Gnostic desire, and it seems inseparable from the other lusts and loyalties at play. Somewhere in that peculiar triangle of thwarted figures, physics does indeed take place.

In the midst of the book's gothic excess, Ms. Goldstein might seem to be declaring the physicists' desire doomed. But I think not. It just may not ever be possible to fully lift it outside human triangles, into the realm of ''icy bliss'' the young physicist seeks.

In the meantime, this book gives it a place in the seat of love and makes it inseparable from the attractions of human bodies.

CAPTIONS: Photo: In ''Bringing Up Baby,'' the impulsive Katharine Hepburn and the detached Cary Grant get together only when the old bones of science collapse. Today, the dichotomy of love and knowledge is breaking down. (Photofest)